相关论文: Duplication Distance to the Root for Binary Sequen…
We study pattern densities in binary sequences, finding optimal limit sequences with fixed pattern densities.
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
The central problem in sequence reconstruction is to find the minimum number of distinct channel outputs required to uniquely reconstruct the transmitted sequence. According to Levenshtein's work in 2001, this number is determined by the…
Results of an exhaustive search for minimum peak sidelobe level binary sequences are presented. Several techniques for efficiency implementation of search algorithm are described. A table of number of non-equivalent optimal binary sequences…
It is well known that, given \(b\ge 0\), finding an $(a,b)$-trapping set with the minimum \(a\) in a binary linear code is NP-hard. In this paper, we demonstrate that this problem can be solved with linear complexity with respect to the…
The paper considers various formalisms based on Automata, Temporal Logic and Regular Expressions for specifying queries over sequences. Unlike traditional binary semantics, the paper presents a similarity based semantics for thse…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
We establish an explicit link between depth-3 formulas and one-sided approximation by depth-2 formulas, which were previously studied independently. Specifically, we show that the minimum size of depth-3 formulas is (up to a factor of n)…
Schmidt proved in 2014 that if $\varepsilon>0$, almost all binary sequences of length $n$ have peak sidelobe level between $(\sqrt{2}-\varepsilon)\sqrt{n\log n}$ and $(\sqrt{2}+\varepsilon)\sqrt{n\log n}$. Because of the small gap between…
The trace reconstruction problem studies the number of noisy samples needed to recover an unknown string $\boldsymbol{x}\in\{0,1\}^n$ with high probability, where the samples are independently obtained by passing $\boldsymbol{x}$ through a…
We consider distance labeling schemes for trees: given a tree with $n$ nodes, label the nodes with binary strings such that, given the labels of any two nodes, one can determine, by looking only at the labels, the distance in the tree…
Low correlation (finite length) sequences are used in communications and remote sensing. One seeks codebooks of sequences in which each sequence has low aperiodic autocorrelation at all nonzero shifts, and each pair of distinct sequences…
Consider a finite set of sources, each producing i.i.d. observations that follow a unique probability distribution on a finite alphabet. We study the problem of matching a finite set of observed sequences to the set of sources under the…
Complementary symmetric Rote sequences are binary sequences which have factor complexity $\mathcal{C}(n) = 2n$ for all integers $n \geq 1$ and whose languages are closed under the exchange of letters. These sequences are intimately linked…
Rotation distance measures the difference in shape between binary trees of the same size by counting the minimum number of rotations needed to transform one tree to the other. We describe several types of rotation distance where…
Insertion-deletion codes (insdel codes for short) are used for correcting synchronization errors in communications, and in other many interesting fields such as DNA storage, date analysis, race-track memory error correction and language…
Nanopore sequencers are emerging as promising new platforms for high-throughput sequencing. As with other technologies, sequencer errors pose a major challenge for their effective use. In this paper, we present a novel information theoretic…
Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
Consider a set $P$ of $n$ points in $\mathbb{R}^d$. In the discrete median line segment problem, the objective is to find a line segment bounded by a pair of points in $P$ such that the sum of the Euclidean distances from $P$ to the line…